Thursday, February 16, 2006

Stocks, flows, and Greenland's glaciers

ABC News reported today on NASA's research that shows Greenland's glaciers melting at twice the rate of only five years ago. That's seemingly another in a long litany of bad news we read, and yet we don't seem to react very quickly.

I've written before about the importance of differentiating between stocks and flows. Let me use this bit of news to illustrate how that can help with an abecederian analysis of global warning (I encountered that word earlier today, and I've been looking for an opportunity to use it!).

Image of four stocks in a chain: human activity level, greenhouse gases, ozone layer coverage, and Greenland ice

Here's my simple (simplistic) mental model showing how I make initial sense of this news story. There's a lot of ice in Greenland, represented above by the stock (rectangle) called Greenland Ice. A stock, as you may recall from my previous posting on the subject, is an accumulation of something. There's a flow into and out of that stock, and I've called it change in ice pa, where pa stands for "per annum" (per year).

In my mind, based on news stories I've read, that ice is melting to a significant degree because of increased insolation, and that increased insolation comes from a reduction in the coverage of the earth's atmosphere with ozone, shown here as another stock.

The Ozone Layer Coverage has flows adding and subtracting to it. Since the news is full of stories describing ozone holes, I imagine the problem is due to excess reduction in the ozone, and news stories suggest increased Greenhouse Gases are at fault.

News stories also pin the blame on the increase in greenhouse gases pa on increased levels of human activity: burning fuels that give off carbon dioxide seems to be a major culprit.

Why is that of concern? As I've written before, scientists are concerned that melting of Greenland's glaciers can lead to a shutting down of the Atlantic conveyor, and that can lead to a rapid cooling of Europe.

Why am I and others concerned, though? Those of you with a bit of a mathematical background and a bit of experience with system dynamics, the field that uses the symbols I've used here, may recognize that this model has four levels of cascaded integration between the input we can control directly (Desired Human Activity Level) and the thing we want to control (Greenland Ice). Each integration adds a delay, which means that changes we make today may not be felt in Greenland for quite a long time. Indeed, even if we make major changes in the input, some of the stocks up the chain may still increase for years until the effect ripples through.

A good study would go further than this abecedarian approach. It would quantify the stocks and flows, check the structure against good scientific insight, and simulate the model to see if it gets results similar to what we've observed in the real world. Nonetheless, even this simple start can identify why there is a concern and help structure thought about ways to address it (and when to decide to address it).

Does that help illuminate stocks and flows? For me, they seemed to allow me to structure my thoughts quickly and usefully.


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